Question

In a survey of 400 students in a school , 110 were listed as taking apple juice and 140 as taking orange juice and 85 were as taking both apple and orange juice as well .Find out how many students were taking neither apple juice nor orange juice. .​

Answer 1

$\sf {\underline{\underline{Answer :-}}}$

$<b>Number of students taking neither apple juice nor orange juice are 235 students</b>$

$\sf {\underline{\underline{Explanation :-}}}$

$\sf {\underline{\underline{Given :-}}}\\\\\\ \sf {Total \: number \: of \: students n(A union B)= 400 \: students}\\\\\\ \textsf {Number of students taking apple juice n(A) = 110 students} \\\\\\ \textsf {Number of students taking orange juice n(B)= 140 students} \\\\\\ \sf {Number \: of \: students \: taking \: both \: apple \: and \: orange \: juice} \\ \sf{n(A intersection B)= 85 \: students} \\\\\\ \textsf {Let number of students taking neither apple juice nor orange juice be x} \\\\\\ \textsf {According to the Question,}\\\\\\ \textsf{\implies n (A\: union\: B ) = n (A) + n (B) - n ( A \:intersection\: B) + x}\\\\\\ \sf {\implies 400 = 110 + 140 - 85 + x}\\\\\\ \sf{\implies 400 = 165 + x}\\\\\\ \sf {\implies x = 400 - 165}\\\\\\ \sf {\implies x = 235} \\\\\\ \textsf{\therefore Number of students taking neither apple juice nor orange juice = 235 students}$